This invention relates to novel processes for hydrocracking a hydrocracking feedstock to produce lighter, branched hydrocarbons with higher octane number than the components of the feed. The processes employ novel solid superacid catalysts, prepared according to a novel process utilizing at least two calcination steps. These catalysts have been found to be effective in a wide variety of catalytic processes in the presence of hydrogen, including isomerization and naphtha upgrading of hydrocarbon feeds.